Части круга и геометрические определения · Повышенный уровень
Введено| English | Значение |
|---|---|
| segment/ˈseɡmənt/ | круговой сегмент |
A round window can be split by a straight chord or by two radii. These cuts create different regions, even though both use a curved boundary.
- A round window can be split by a straight chord or by two radii. These cuts create different regions, even though both use a curved boundary.
- This lesson studies segment 弓形: A region bounded by a chord and its corresponding arc.
Choose the mathematical structure
- A circle consists of points a fixed radius from its centre. A diameter is a chord through the centre and has length 2r. A chord joins two circumference points; an arc is part of the circumference. A sector lies between two radii and an arc. A segment lies between a chord and an arc. A tangent touches at one point and is perpendicular to the radius there.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Какая граница определяет сегмент круга?
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Отрезок, отсекаемый хордой. Два радиуса с дугой образуют сектор — прямые стороны отличаются, именно это проверяют вопросы на периметр.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
For centre O and radius 5 cm, every circumference point is 5 cm from O and the diameter is 10 cm. A chord 3 cm from O has half-length √(5²-3²)=4 cm, so its whole length is 8 cm. The perpendicular from O meets the chord at its midpoint. Joining the two chord endpoints to O creates a sector; the smaller region between chord and arc is a segment. At the rightmost circumference point, the vertical touching line is tangent and the horizontal radius is perpendicular to it. The circumference is a length, 2πr=10π cm, rather than an area.
Части круга и геометрические определения
Круг состоит из точек, находящихся на фиксированном расстоянии (радиусе) от его центра.
Классифицируйте утверждения из разобранного примера, затем объясните единицы измерения или инвариант, обосновывающий каждое решение.
Найдите диаметр, если радиус равен 5 см.
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Диаметр=2×5=10 см.
Test a tempting shortcut
- A chord need not pass through the centre; only a diameter must. Sector and segment have different straight boundaries. Do not confuse circumference length with the shaded area inside a circle.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
A sector is bounded by a chord and an arc. This claim is false. Explain which definition or assumption it violates.
Найдите половину хорды для радиуса 5 и перпендикулярного расстояния от центра до хорды 3.
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Используйте √(25-9)=4 см.
Сектор ограничен хордой и дугой.
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Хорда не обязательно проходит через центр; только диаметр должен. Сектор и сегмент имеют разные прямые границы. Не путайте длину окружности с заштрихованной областью внутри круга.
Interpret a new situation
- AQA G9 includes all named circle parts at Foundation. Use the given radius and position labels to identify the part; Higher circle-theorem proofs are developed separately.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Найдите полную длину хорды в этом примере.
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Перпендикуляр делит хорду пополам: 2×4=8 см.
Сопоставьте каждую часть круга с её определением.
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Диаметр — это особая хорда, проходящая через центр; сектор и сегмент различаются своими прямыми границами.
Use this in your course
- 8300 · Higher · 3.4. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
A region bounded by a chord and its corresponding arc. Choose the relationship, show the method, check its assumptions and interpret the result.